In earthworking machines, it is common to have machines, such as those represented in U.S. Pat. No. 6,140,787, that are fitted with an articulated arm on a self-propelled assembly, with the articulated arm being controlled by hydraulic jacks and following a modifiable trajectory, at the end of which is positioned an excavation tool or a similar tool such as a bucket, itself controlled in an angular position by a hydraulic jack. Angle sensors positioned with precision on the articulations of the machine arms, as is the case in document U.S. Pat. No. 6,140,787, or fixed onto the arm, are used to determine the angles between the machine and the first articulated element forming the arm, between the first and the second articulated elements forming the arm, and between the second articulated element forming the arm and the tool. Knowing these angular values and the exact dimensions of the elements forming the articulated arm of the machine between the different articulation points of the arm, it is perfectly possible to control the movements of the machine by means of control levers that are used to determine the movements of the hydraulic jacks and, as a consequence, to determine the position of the bucket. In such devices however, it is necessary to perform a calibration of the control circuits of the machine in order to be sure of the final position of the bucket, even when one precisely knows the angles and lengths of the articulation elements forming the arm.